WO2025158137A1

WO2025158137A1 - Correcting optical aberration

Info

Publication number: WO2025158137A1
Application number: PCT/GB2025/050097
Authority: WO
Inventors: Chao He; Zimo ZHAO; Yifei MA; Steve Elston; Stephen Morris; Martin Booth
Original assignee: Oxford University Innovation Ltd
Current assignee: Oxford University Innovation Ltd
Priority date: 2024-01-23
Filing date: 2025-01-21
Publication date: 2025-07-31
Anticipated expiration: 2026-07-23
Also published as: GB202400861D0

Abstract

A method of correcting for an aberration in an optical system (600) comprising an imaging detector (634) having a focussing lens (608) and a spatial light modulator (610) is provided. The method comprises receiving an image. The method comprises determining an intensity aberration compensation from the collected image. The method comprises controlling the spatial light modulator (610) to reduce the intensity aberration by applying the intensity aberration compensation.

Description

CORRECTING OPTICAL ABERRATION

TECHNICAL FIELD

The present invention relates to correcting for an aberration in an optical system.

BACKGROUND

Aberrations in optical images may be introduced by imperfections in an imaging system (for example, a microscope) and by an inhomogeneous refractive index of imaged objects (or of a medium between the object and the imaging system) . Aberrations are distortions of the optical wavefront that affect image quality by reducing signal level, contrast and resolution. Types of optical aberrations include intensity, phase and polarisation aberrations.

Adaptive optics (AO) is a powerful tool that is widely used to correct such aberrations in a range of contexts such as astronomical telescopes, optical communications, and super-resolution microscopy/nanoscopy. AO has historically been focused on phase aberration correction. Recently, AO has encompassed polarisation adaptive optics (P-AO), used for polarisation aberration correction, and vectorial adaptive optics (V-AO), used for both polarisation and phase aberration correction.

Although considerable progress has been made in the field of adaptive optics, there is room for improvement. The present invention has been devised with the foregoing in mind.

SUMMARY

According to a first aspect, there is provided a method of correcting for an aberration in an optical system comprising an imaging detector having a focussing lens and a spatial light modulator on an object side of the focussing lens. The method comprises receiving an image. The method further comprises determining an intensity aberration compensation from the received image (which may instead be referred to as the collected image). The method also comprises controlling the spatial light modulator to reduce the intensity aberration by applying the intensity aberration compensation.

The spatial light modulator may be the object side of the focussing lens, for example at the back focal plane of the focussing lens, or more generally in a pupil plane (on the object side of the focussing lens and normal to the optical axis of the focussing lens).

Various intensity aberrations and their effects exist among modern optical systems - they can be induced via the light sources themselves, due to Fresnel’s effects occurring within the optical pathway, non-uniform diattenuation effects, or absorption effects within materials or biological tissues. These issues directly alter the intensity value and uniformity across the pupil plane, and affect systematic performance.

Intensity aberrations can lead to non-perfect focus spots due to imperfect interference at the focal plane (at the imaging detector). For example, in microscopy, an intensity aberration can cause a decrease in image resolution due to the non-perfect interference at the focal plane, and the image contrast may be decreased because of energy loss and a higher signal to noise ratio. Intensity aberration correction can therefore provide an important complementary tool for AO.

The method may further comprise reducing a phase aberration.

Reducing a phase aberration may use a further spatial light modulator, such that the further spatial light modulator is configured to modulate a spatial variation of phase at the pupil plane.

The further spatial light modulator may be a deformable mirror.

Reducing a phase aberration at the pupil plane may also use the spatial light modulator, such that that the spatial light modulator may be used to reduce both phase aberration and intensity aberration at the pupil plane.

Correcting for phase aberration at the pupil plane may be subsequent to the step of controlling the spatial light modulator to reduce the intensity aberration at the pupil plane by applying the intensity aberration compensation, so that the reduction of phase aberration may be performed after the reduction of intensity aberration.

The method may further comprise adjusting an attenuator to compensate for any change in average intensity at the imaging detector arising from reducing intensity aberration and/or reducing phase aberration.

The step of receiving an image may comprise obtaining an image with a pupil sensor at the pupil plane, arranged to directly detect the intensity aberration.

Receiving an image may comprise obtaining an image from the imaging detector and the intensity aberration may be inferred from one or more images obtained at the imaging detector.

The method step of determining an intensity aberration compensation at the pupil plane may comprise configuring the spatial light modulator to apply each of a plurality of pre determined aberration correction patterns. The method may further comprise, for each pre-determined aberration correction pattern, obtaining an image from the imaging detector. The method may also comprise determining a performance metric for each of the images obtained for each pre -determined aberration correction pattern. The method may also comprise determining the intensity aberration compensation from the determined performance metrics.

The plurality of pre-determined correction patterns may comprise piston, tip, tilt and/or defocus intensity Zernike modes.

The method may further comprise providing a known pattern to be imaged at the imaging detector during the method step of receiving an image. The performance metric may based on a similarity between the image at the imaging detector obtained in receiving an image with the known pattern to be imaged.

According to a second aspect, there is provided a system comprising an optical system comprising an imaging detector having a focussing lens, and a spatial light modulator on an object side of a focussing lens . The system further comprises a processor configured to receive an image from the optical system. The processor determines an intensity aberration compensation at a pupil plane from the received image and controls the spatial light modulator to reduce the intensity aberration by applying the intensity aberration compensation.

The pupil plane may be defined as on the object side of the focussing lens and normal to the optical axis of the focussing lens .

The system of the second aspect may be configured to perform the method of the first aspect, including any optional features thereof. Features of the example embodiments may be combined with any aspect.

According to a third aspect, there is provided a non-transitory computer readable medium comprising instructions which, when the program is executed by a processor, cause the processor to carry out the method of the first aspect, including any optional features thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described, by way of example only, with reference to the accompanying drawings in which:

Figure 1 shows how an intensity aberration can lead to a distortion of focus;

Figure 2 shows an optical system comprising a spatial light modulator configured to apply an intensity aberration compensation;

Figure 3 shows an optical system comprising a spatial light modulator configured to apply an intensity compensation, and a further spatial light modulator configured to modulate a spatial variation of phase at a pupil plane;

Figure 4 shows a sensor-based optical system for correcting aberration in the optical system, comprising an imaging detector and a spatial light modulator, according to an embodiment of the invention ; Figures 5a to 5d show a graphical representation of how sensor-based intensity aberration correction can be successfully implemented to correct an intensity aberration;

Figure 6 shows an optical system comprising an imaging detector and a spatial light modulator, according to an embodiment of the invention ;

Figure 7 shows show a graphical representation of how sensorless -based intensity aberration correction can be successfully implemented to correct an intensity aberration;

Figures 8a and 8b show example intensity Zernike modes and corresponding corrections for unintended phase modulation;

Figure 9 shows a method for sensor-based intensity aberration correction; and Figure 10 shows a method for sensorless intensity aberration correction.

Like reference numbers and designations in the various drawings may indicate like element

DETAILED DESCRIPTION

Figure 1 shows how an intensity aberration can lead to a distorted focus spot 105. Light of uniform intensity 102 passes through a source of intensity aberration 104, resulting in light of distorted intensity 103 after the source of intensity aberration 104. The light of distorted intensity 103 is incident on a focussing lens 108. After passing through focussing lens 108, the intensity aberration results in a distorted focus spot 105.

In a representative example, the light source may be a microscopy sample on a slide. The objects to be imaged may be particles within an at least partially transparent medium (e.g. an aqueous fluid). Light passing from the light source to the optical system may pass through the sample in order to reach the imaging sensor of any imaging system. The sample may impose aberrations : both phase aberrations (for example, resulting from a spatial variation in refractive index) and intensity aberrations (for example, resulting from a spatial variation in light attenuation). There may be further sources of aberration in the optical system between the sample and the imaging detector. For example, a deformable mirror configured to impose a spatial modulation of phase (for adaptive optics) may introduce an amount of intensity aberration.

This example scenario is merely illustrative, and it will be understood that similar issues are present in other imaging scenarios. For example in optical imaging of distant objects through the atmosphere, the atmosphere is a source of aberration.

Figure 2 shows an optical system 200 comprising: a spatial light modulator 210, source of intensity aberration 204, focussing lens 208 and imaging detector 214. Input light 202 (e.g. of uniform intensity, as depicted in Figure 2) passes through the spatial light modulator 210. The spatial light modulator 210 is configured to alter the spatial variation of intensity of the input light 202 such that the output light 206 from the spatial light modulator has a pre-compensated spatial variation in intensity 206. The spatial variation of intensity imposed by the spatial light modulator 210 is selected so that aberrations in intensity are corrected at a back focal plane of the focussing lens 108.

In this example, a source of intensity aberration 204 may be a sample 204 between the spatial light modulator 210 and the focussing lens. The sample 204 imposes an intensity aberration on the light passing through it. The intensity aberration imposed by the spatial light modulator 210 is selected to compensate for the sample 204, so that corrected light (with corrected spatial variation of intensity) 212 is present following the intensity aberration source 204. The corrected light 212 can then pass through focussing lens 108 to generate an ideal (or more ideal) focus spot 214. The corrected light 212 results in a more ideal image on the imaging detector after the focussing lens 208.

In other embodiments, at least some of the source of intensity aberration may be at least partly prior to the spatial light modulator 210. The spatial light intensity modulator 210 preferably does not modify the spatial variation of phase.

Figure 3 shows an optical system 300, illustrating some of the features described in Figure 2 in more detail. The optical system 300 comprises intensity aberration corrector 310 and phase aberration corrector 324. Input light is depicted as having uniform intensity 302 and phase 314. The input light passes through the intensity aberration corrector 310 which applies an intensity compensation. The light from the intensity aberration corrector 310 is subsequently received by the phase aberration corrector 324, which modifies the spatial variation of phase to correct for aberrations in phase in the optical system. The output from the intensity aberration corrector 310 has pre -corrected intensity 306 and may have distorted phase 322. The output from the phase aberration corrector 324 has pre-compensated intensity 312 and uniform phase 326.

The intensity aberration corrector 310 comprises a spatial light modulator 318 sandwiched between crossed linear polarisers 316. The spatial light modulator 318 comprises a liquid crystal 319 sandwiched between a pair of transparent sheets 317. Electrodes are disposed on the transparent sheets for selectively applying a field across different spatial regions of the liquid crystal 319. The birefringence of the liquid crystal 319 can be consequently modified in different regions of the liquid crystal. The effect of varying the birefringence is to modify the polarisation characteristics of the light. The input polarising filter has a polarisation orientation at +45 degrees to an alignment direction of the liquid crystal, and the output polarising filter has a polarisation orientation at +45 degrees to the alignment direction. The transmittance T of light through the spatial light modulator 318 can be expressed as: where x is the angle between the polarisers and the alignment direction of the liquid crystal, which is 45 degrees, A is the wavelength of the incident light, d is the distance light travels through the liquid crystal layer, and An is the birefringence of the nematic liquid crystal between its two optical axes (which is modulated by applied field). The electrodes are configured to comprise a plurality of pixels, so that the modulation of intensity imposed by the spatial light modulator can be adjusted on a per-pixel basis. The liquid crystal may have any suitable phase, for example, nematic, chiral nematic, etc.

A suitable spatial light modulator (SLM) may be digitally controlled. An n-bit (e.g. 8- bit) grey-scale image may be used as an input to define a modulation to be applied by the SLM 318. The resolution of the image will match the resolution of the SLM 318. A pre-determined mapping may be determined between an image value and a voltage across each pixel. In order to get a precise and fast control of the modulated intensity within a limited time frame during the correction process, it may be useful to obtain a look-up-table (LUT) to determine the relationship between the SLM pixel values and modulated intensity for a quick derivation of the pattern to be loaded onto the SLM. To get LUT values for each pixel of the SLM, the following steps may be adopted to extract the intensity modulation range of the SLM pixels. First, the initial intensity of the source light (e.g. a laser, for producing a point of light) is adjusted using a neutral density filter, and the exposure time of a camera located at the pupil plane (for example, at the back focal plane of a focussing lens of an imaging detector) is selected to ensure that the calibration data will use the full dynamic range of the camera. Once determined, the light intensity and the camera exposure time are fixed while the pixel intensity response is determined. Although the pupil plane may be at the back focal plane of the focussing lens, it may also be in other suitable positions on the object side of the focussing lens.

To efficiently obtain all the pixel intensity responses, a uniform image with one single value (so called ‘flat value’) across all pixels may be utilized. For an SLM with an 8- bit modulation depth, flat values Fj satisfying Fj G [0,255], Fj G Z may be examined. Each flat value Fj was applied across the SLM and the intensity values across the pupil plane of the SLM recorded.

It should be noted here that the SLM patterns calculated from the captured images (from the camera at the pupil plane) may not be a direct mapping to the SLM pixels, as the number and size of pixels on the SLM may not be identical to image captured by the CCD camera. However, this can be easily overcome by performing an interpolation to map the captured images size to the resolution of the SLM, or vice versa. Thus, the corresponding intensities P_in on the pupil plane across all N pixels assigned with the flat value Fj will be derived as [F^, Pj₂, ... Pj_W]. This process can be performed iteratively until all the flat values Fj are applied and their corresponding pupil image values are recorded. For the intensity modulation range of each pixel n C N, the intensities [Pon> in> ■■■ 255n\ ^can be derived from the measurement. The relationship between modulation value and intensity is typically well approximated by a trigonometric function.

To ensure a unique mapping between flat values and the intensities, the flat value F_Sn with a minimum intensity value S_n and the flat value F_inwith a maximum intensity value L_n of the dynamic range data should be identified. S_n and L_n are the index i of Fj for pixel n C N. The intensity values between the minimum value S_n and the maximum value L_n with their corresponding flat values between F_Sn and F_Ln will be used in the intensity aberration compensation process, and other values outside this range will be unwrapped for a linear response. After these processes, the mapping between flat values Ft and the intensity values P_in for each pixel n will have a linear relationship. These linear mapping will then be saved into a LUT together with the minimum values S_n and the maximum values L_n indicating the valid pixel value ranges.

In this example the spatial light modulator 318 is depicted as a chiral/twisted nematic liquid crystal spatial light modulator, but any suitable technology for the spatial light modulator can be used. Although phase modulation by the intensity aberration corrector 310 may be small, at least some of the phase aberration that is corrected by the further spatial light modulator 324 may arise from the spatial light modulator 318. Correction for this unintended phase modulation is discussed below.

Figure 4 shows a sensor-based adaptive optics system 400, comprising: an (optional) attenuator 430, intensity aberration corrector 410, sample 404, pupil intensity sensor 432, focussing lens 408 and imaging detector 434. This embodiment is illustrative of a sensor-based approach to intensity aberration correction. In the sensor-based approach, a known object may be positioned on the object side of the system. For example, an aperture and a light source (or a point source of light, such as a laser) can be used to create a bright spot on the object side to be imaged by the system. In an optical system without aberration, the spot can be expected to produce an Airy function, for example, in the centre of the imaging detector at the front focal plane of the focussing lens.

The pupil intensity sensor 432 is disposed in the pupil domain of the focussing lens 408 (e.g. at the back focal plane) and collects an image which indicates a variation of intensity at the pupil plane. The intensity aberration is then determined from the collected image by a processor (not shown) and used to determine an intensity aberration compensation (e.g. by finding a difference between an expected image at the pupil intensity sensor 432 and the collected image).

The spatial light modulator of the intensity aberration corrector 410 is controlled through feedback loop SI to apply the intensity aberration compensation to the image at the input of the spatial light modulator 410, to generate a light field that has precompensated intensity variation. The pre-compensated light can then pass through the sample 404 to generate a corrected image substantially free from intensity aberration. The image of corrected intensity can then pass through focussing lens 408 to generate an ideal focus spot at the imaging detector 434.

An optional further feedback loop may be provided, in which the attenuator 430 is controlled, responsive to the intensity aberration determined by the pupil intensity sensor 432, such that the attenuator compensates for any change in average intensity at the imaging detector arising from reducing intensity aberration and/or reducing phase aberration.

Figures 5a to 5d show results obtained from sensor-based intensity adaptive optics.

In the experiments of Figure 5a-d, the object was a point of light, which should result in a focussed spot (Airy disk) on the imaging detector. An intensity spatial light modulator SLM1 (e.g. such as the SLM 318, described with reference to Figure 3) was used as part of an intensity aberration corrector, and a further SLM2 was used as a source of intensity aberration (e.g. taking the role of intensity aberration source 204 in Figure 2). Initially, SLM1 and SLM2 were set to flat - imparting no spatial variation in intensity. Images were captured from a pupil intensity detector and from an imaging sensor (at the front focussing plane of the focussing lens). A conventional AO phase correction process was subsequently applied to correct for phase aberration caused by various components of the optical system. The intensity distribution at the imaging sensor with no aberration applied by SLM2 comprises (or is well approximated by) an Airy disk. A random aberration can be applied using SLM2 - in the form of a pattern comprising an arbitrary combination of Zernike modes of intensity modulation.

Figures 5a and 5b illustrate the effect of intensity aberration with phase correction (but without intensity aberration correction) . In the first column of Figure 5a, the image (intensity) at the pupil (top) and at the imaging detector (bottom) are shown with intensity aberration applied by SLM2. The focal spot at the imaging detector is distorted (bottom) and there is intensity aberration at the pupil (top). The second column of Figure 5a shows results obtained with the intensity aberration applied on SLM2, and phase correction AO turned on (with no intensity aberration correction). A map of the phase correction applied by the phase correcting spatial light modulator (e.g. deformable mirror) is shown (top) and the resulting image at the imaging detector is shown (bottom). The phase correcting AO does not remove the distortion of the image. In the third column of Figure 5a, the intensity aberration applied by SLM2 is turned off, leaving the phase correcting AO turned on. The resulting image at the pupil (top) and imaging detector (bottom) show that the focussed spot is not distorted at the imaging detector.

The variation in intensity in the bottom images of Figure 5a can be more clearly seen in Figure 5b, which shows a graph with curves obtained sampling the intensity along a horizontal diameter of the bottom image of each column in Figure 5a. The legend is captioned “I-AO off’ corresponding with the first column of Figure 5a, “Phase AO on” corresponding with the second column of Figure 5a, and “Aberration removed” corresponding with the third column of Figure 5a.

It can readily be seen that the intensity aberration is not corrected in the second column, and that when intensity aberration is not present, the point spread function is close to an Airy function.. The curve corresponding with the right column in Figure 5b can be thought of as a reference or target for intensity aberration correction in this example system.

Figure 5c illustrates the operation of sensor-based intensity aberration correction in which a first feedback loop (S I in Figure 4) is used to determine a spatial variation of intensity modulation to apply at an intensity aberration corrector and a second (optional) feedback loop (S2 in Figure 4) is used to determine an appropriate setting for an attenuator (adjusting an overall brightness upward or downward, without spatial variation).

The images in the columns of Figure 5c respectively show results obtained with an intensity aberration applied (at SLM2) and: i) no correction for intensity aberration or phase aberration; ii) intensity correction (S I loop) but no overall brightness correction (no S2 loop) and no phase correction ; iii) phase correction and intensity correction (SI only); iv) phase correction and intensity correction (SI and S2). In columns i), ii) and iv) the top row shows an intensity image at the pupil intensity detector and the bottom row shows an intensity image at the imaging detector. In column iii) the top row shows a phase correction applied at a phase correcting spatial light modulator and the bottom row shows an intensity image at the imaging detector.

Figure 5d shows curves extracted from the bottom row of images in Figure 5c, in the same way as described with reference to Figure 5b. The legend has captions corresponding with the column headings in Figure 5c

After the first intensity correction loop (results shown in column iii)) it is clear that the distortion of the image resulting from intensity aberration has been remedied, but there is a substantial change in intensity (when compared with the reference curve in Figure 5b). The second correction loop removes this change in overall intensity, and the shape of the curve corresponds with the reference that is obtained with no intensity aberration in the system.

Figure 6 illustrates an optical system 600 comprising: an (optional) attenuator 630, intensity aberration corrector 610 (comprising a spatial light modulator), source of intensity aberration 604, focussing lens 608 and imaging detector 634. This example is illustrative of a sensorless approach to intensity correction. A phase correcting spatial light modulator may also be present (not shown).

In the sensorless approach, an appropriate intensity correction is determined from the imaging detector 634 (eliminating the need for a pupil intensity detector). An example approach for determining an intensity aberration from data obtained from the imaging detector is outlined below.

An image is collected at the imaging detector 634. The intensity aberration, introduced by source of intensity aberration 604, is inferred from one or more images obtained at the imaging detector 634. The inferred intensity aberration is then used to control the spatial light modulator 610 through first feedback loop SL1 and optionally the attenuator through a second feedback loop SL2.

The spatial light modulator may be configured to apply each of a plurality of predetermined aberration correction patterns. For each pre-determined aberration correction pattern, an image is obtained from the imaging detector. A performance metric is determined for each of the obtained images . One or more aberration correction patterns may be selected as the optimal correction pattern based on the performance metric.

The performance metric may be based on a similarity between an expected image at the imaging detector (e.g. an Airy function or other expected point spread function resulting from a point of light in the object space).

A set of standard modes (or patterns) may be used to estimate the aberration at the pupil plane by evaluating images obtained at the front focal plane of the focussing lens. Unlike the a phase profile, a normalised intensity modulation has a limited range from 0 to 1 and cannot be wrapped (unlike phase, where values wrap to a range of — n to +TT). Thus, the standard mode patterns used in an intensity aberration correction sensorless algorithm will be different from the ones used for a conventional wavefront (phase) sensor less correction algorithm. Any suitable set of basis functions can be used to approximate the aberration correction - for example, based on Zernike modes, cosine functions, sin functions, wavelet transforms etc.

Zernike modes (applicable for phase correction, with a range of -1 to +1) may be modified into a series of intensity Zernike modes whose ranges are limited between 0 and 1. These intensity Zernike modes may be applied using an intensity aberration corrector comprising a SLM sandwiched by a pair of polarizers (as described with reference to Figure 4). Because of the geometric link between intensity and phase via the SLM modulation, extra phase aberrations may introduced by the SLM of the intensity aberration corrector. These extra phase aberrations can be cancelled out using a phase correcting spatial light modulator (e.g. comprising one or more deformable mirrors). The intensity correction pattern loaded onto the intensity correcting SLM, and the phase correction pattern loaded onto the phase correcting SLM may form a pair of patterns used for sensor-less correction.

A modified intensity Zernike modes (with a range of 0 to 1) Z with index m and n can be expressed as -( e) = _crf^l (p)0-(e) where: cm _ 1 n -¹-

One method for finding an appropriate intensity aberration correction is to: i) select a Zernike mode; ii) vary the scale of the current Zernike mode over a range using a scaling factor in a predetermined number of steps and apply the values of the scaled Zernike mode as a spatial intensity modulation using a spatial light modulator; iii) record an image from the imaging detector for each of the steps in ii); iv) reset the spatial intensity modulation to zero; v) select a different Zernike mode, and repeat steps ii) to iv).

Resetting the intensity modulation before scanning the next Zernike mode is important because it means that the intensity on the pupil plane will always be in the linear region and below the saturation level. In the example results presented herein 15 Zernike modes are examined (with Noll index from 1 to 15), and the corresponding scaling factor is scanned from 0.025 to 0.975 with 11 steps for each Zernike mode. These Zernike modes comprise piston, tip, tilt and defocus modes. All images from the imaging detector for each mode are recorded.

Example intensity Zernike modes are depicted in Figure 8 a. For each Zernike mode at the intensity spatial light modulator, a modulation of phase (which is unintended) may result. A relationship between the intensity modulation and accompanying phase modulation may be determined (e.g. empirically or theoretically), and a phase spatial light modulator used to remove any phase modulation from the intensity spatial light modulator. Figure 8b illustrates, for Noll index 802 of 4, an intensity pattern 804 to be applied on the intensity spatial light modulator and a phase pattern 806 to be applied at a phase spatial light modulator (e.g. deformable mirror) to cancel unintended phase modulation by the intensity spatial light modulator.

To find the best mode (or modes) for correcting the intensity aberration and (optionally) blending more than one mode into a suitable pattern, a performance metric determined for each of the images (corresponding with a candidate correction pattern) . The idea is to find which intensity Zernike mode (Noll index) with what scaling can best correct image on the imaging detector. The performance metric can be based on a number of criteria - such as image sharpness, local contrast etc. When the image is a point spread function (e.g. an Airy function) corresponding with an image of a point light source in the object side, spot circularity can be used, as well as algorithms based on spatial frequency.

In an example experiment, it was observed the Zernike modes with Noll indices of 6 and 9 provided the best correction result. In order to simplify the final correction process, a single mode (with Noll index 6) was utilised for correction. The best combination of mode and scaling factor may be applied to correct intensity aberration. After the intensity aberration is corrected in this way, a phase AO correction algorithm may be executed again to add any further phase correction that is required.

Similar to the sensor-based approach, in a proof of principle system, the intensity aberration corrector comprises SLM1 and the source of intensity aberration 604 comprises a further SLM2 arranged to spatially modulate intensity.

Figure 7a and 7b show example results obtained by sensorless-based intensity aberration correction, with a similar test process as used for the sensor-based approach shown in Figures 5a to 5d.

The columns of Figure 7a correspond with: i) an intensity aberration introduced by the source of intensity aberration, no phase aberration correction and no intensity aberration correction; ii) an intensity aberration introduced by the source of intensity aberration, phase aberration correction activated and no intensity aberration correction; iii) an intensity aberration introduced by the source of intensity aberration, phase aberration correction activated and sensorless aberration correction loop SL1 activated (no overall intensity correction); and iv) an intensity aberration introduced by the source of intensity aberration, phase aberration correction activated and sensorless aberration correction loop SL1 and SL2 activated (i.e. with overall intensity correction).

For column i) the image in the top row of Figure 7a shows the variation in intensity at the pupil (although no pupil intensity sensor is used in the sensorless approach it is still instructive to measure the pupil intensity image for this demonstration). The top row for columns ii) to iv) of Figure 7a otherwise show the phase correction applied by the phase correcting spatial light modulator. The bottom row of images in Figure 7a show the images obtained from the imaging detector - which should ideally correspond with an Airy function.

The variation in intensity in the bottom images of Figure 7a can be more clearly seen in Figure 7b, which is a graph with curves obtained by sampling the intensity along a horizontal diameter of the bottom image of each column in Figure 7a. The legend is captioned “I-AO off’ corresponding with the first column of Figure 7a, “Phase AO on” corresponding with the second column of Figure 7a, “I-AO SL1 on” corresponding with the third column of Figure 7a, and "I-AO SL2” on” corresponding with the fourth column of Figure 7a

The information shown in Figure 7a and 7b show that traditional phase OA is unsuitable for correcting for intensity aberrations, leading to non-perfect focus spots of non- uniform intensity and a lower peak intensity. With the intensity aberration correction applied, the point spread function much better approximates the ideal case, overcoming the limitations of adpative optics that do not include intensity aberration correction.

Sensorless intensity aberration correction has potential to be used in future applications that require both intensity and phase correction where extra hardware for detecting spatial variation of intensity in the pupil domain is limited, such as in complex hardware systems.

Figure 9 shows a method 900 comprising steps of a sensor-based intensity aberration correction. The method 900 comprises generating a sensor-based look up table 910 and performing a sensor-based intensity aberration correction 920. Generating a sensorbased look up table 910 comprises steps of:

902 generating flat values Fj G [0,255], Fj G Z;

904 capturing an image of intensity at a pupil plane at a current value of F^;

906 determine intensity profile [F^, ?^, ... Pj_W] by mapping the image of intensity at the image plane to the pixels of the spatial light modulator ; in loop 905, increment Fj and repeat step 904 until images corresponding with all values of Fj have been captured; 908 find extremums F_Sn and F_Ln from ■ ■■ F⁾ _255n] f°^r each pixel and derive a linear dynamic range.

The system is calibrated at 909 and the sensor-based intensity aberration correction 920 can begin. The sensor-based intensity aberration correction 920 comprises:

922 levelling the spatial light modulator of the intensity aberration corrector to a specific intensity Ptarget using the look up table determined in 910;

921 intensity aberration introduced;

924 capture pupil plane intensity image and calculate the differences for each pixel of the spatial light modulator = P_target - P_Capture<F and

926 apply new target level for each pixel to compensate for intensity aberration Pi ⁼ Ptarget + Pi-

At 925 a phase aberration correction can be performed to more fully correct aberrations in the optical system.

Figure 10 shows a method 950 comprising steps of a sensorless intensity aberration correction. The method 950 comprises steps of:

951 system calibrated (e.g. as described in Figure 9, 910)’

953 aberration introduced;

971 run phase aberration correction (e.g. wavefront sensorless) algorithm to correct phase aberrations and leave intensity aberrations uncompensated;

972 scan the current intensity Zernike mode over a range of scaling factors and record the image (e.g. point spread function) at the imaging detector;

973 reset the intensity spatial light modulator to an initial state;

974 apply the next Zernike mode and repeat steps 972, 973 and 974 until all Zernike modes are scanned;

960 illustrates that, for each increment of the scan in step 972, a spatial variation of intensity 962 is defined for the intensity spatial light modulator and a corresponding spatial variation of phase 964 is applied to a phase spatial light modulator to cancel phase variations resulting from the pattern 962;

975 after scanning all the Zernike modes, determine the best Zernike mode to be applied for intensity aberration correction; 976 optionally, scanning a scaling factor for the best Zernike mode over a more finely divided range of scaling factors than defined in step 972 to refine the best scaling factor for the best Zernike mode;

977 apply the best mode with the best scaling factor and optionally verify that the image obtained from the imaging detector is as expected (e.g. a well corrected point spread function);

978 optionally, perform further correction for phase aberration.

From reading the present disclosure, other variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other features which are already known in the art of adaptive optics, and which may be used instead of, or in addition to, features already described herein.

Although an example method for sensorless intensity aberration correction has been described, other approaches are possible. For example, an appropriate correction can be found using machine learning. For example, a set of training data can be obtained by experiments or simulations performed using a known source of intensity aberration (e.g. a spatial light modulator). An artificial neural network (ANN), such a convolutional neural network, can be trained to take the image (e.g. of a point spread function) which is distorted due to the intensity aberration, and determine the intensity aberration. The training may comprise adjusting model parameters (e.g. kernel weights) in order to minimise a penalty function by backpropagation of errors. The penalty function may be a difference between the known intensity aberration and the predicted intensity aberration from the ANN. Alternatively, an expectation maximisation algorithm may be used in which an iterative method is used to find a maximum likelihood estimate for the intensity aberration (e.g. coefficients/scaling factors for a set of basis functions).

Although the appended claims are directed to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel feature or any novel combination of features disclosed herein either explicitly or implicitly or any generalisation thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. Features which are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. The applicant hereby gives notice that new claims may be formulated to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

For the sake of completeness, it is also stated that the term "comprising" does not exclude other elements or steps, the term "a" or "an" does not exclude a plurality, a single processor or other unit may fulfil the functions of several means recited in the claims and any reference signs in the claims shall not be construed as limiting the scope of the claims.

Claims

1. A method of correcting an aberration in an optical system, the optical system comprising an imaging detector having a focussing lens and a spatial light modulator on an object side of the focussing lens , the method comprising: a) receiving an image; b) determining an intensity aberration compensation from the received image; c) controlling the spatial light modulator to reduce the intensity aberration by applying the intensity aberration compensation.

2. The method of claim 1 , further comprising reducing a phase aberration.

3. The method of claim 2, wherein reducing the phase aberration comprises using a further spatial light modulator, the further spatial light modulator configured to modulate a spatial variation of phase.

4. The method of claim 2, wherein the further spatial light modulator is a deformable mirror.

5. The method of claim 2, wherein reducing a phase aberration comprises using the spatial light modulator to reduce phase aberration , so that the spatial light modulator is used to reduce both phase aberration and intensity aberration .

6. The method of any of claims 2 to 5, wherein correcting for phase aberration is subsequent to step c), so that the reduction of phase aberration is performed after the reduction of intensity aberration.

7. The method of any of claims 1 to 6, comprising adjusting an attenuator to compensate for any change in average intensity at the imaging detector arising from reducing intensity aberration; and/or the method of any of claims 2 to 6, comprising adjusting an attenuator to compensate for any change in average intensity at the imaging detector arising from reducing phase aberration.

8. The method of any preceding claim, wherein the step of receiving an image comprises obtaining an image with a pupil sensor, arranged to directly detect the intensity aberration.

9. The method of any preceding claim, wherein the step of receiving an image comprises obtaining an image from the imaging detector and the intensity aberration is inferred from one or more images obtained at the imaging detector.

10. The method of claim 9, wherein determining an intensity aberration compensation comprises: i) configuring the spatial light modulator to apply each of a plurality of pre determined aberration correction patterns; ii) for each pre-determined aberration correction pattern, obtaining an image from the imaging detector; iii) determining a performance metric for each of the images obtained in step ii); iv) determining the intensity aberration compensation from the results of step iii).

11. The method of claim 10, wherein the plurality of pre -determined correction patterns comprise piston, tip, tilt and/or defocus Zernike modes.

12. The method of claim 10 or 11 , further comprising providing a known pattern to be imaged at the imaging detector during step ii), and wherein the performance metric is based on a similarity between the image at the imaging detector obtained in step ii) with the known pattern to be imaged.

13. A system comprising: an optical system comprising: an imaging detector having a focussing lens, and a spatial light modulator on an object side of the focussing lens ; and a processor configured to: a) receive an image from the optical system; b) determine an intensity aberration compensation from the received image; c) control the spatial light modulator to reduce the intensity aberration by applying the intensity aberration compensation.

14. The system of claim 13, configured to perform the method of any of claims 1 to 12.

15. A non-transitory computer readable medium comprising instructions which, when the program is executed by a processor, cause the processor to carry out the method of any of claims 1 to 12.